Rosenthal and semi-Tauberian linear relations in normed spaces

Teresa Álvarez; Antonio Martínez-Abejón

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 707-722
  • ISSN: 0392-4041

Abstract

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The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related to Rosenthal linear relations in the same way as Tauberian linear relations are related to weakly compact linear relations. We describe examples and investigate special cases: in particular, F + and strictly singular linear relations.

How to cite

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Álvarez, Teresa, and Martínez-Abejón, Antonio. "Rosenthal and semi-Tauberian linear relations in normed spaces." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 707-722. <http://eudml.org/doc/195428>.

@article{Álvarez2005,
abstract = {The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related to Rosenthal linear relations in the same way as Tauberian linear relations are related to weakly compact linear relations. We describe examples and investigate special cases: in particular, $F_\{+\}$ and strictly singular linear relations.},
author = {Álvarez, Teresa, Martínez-Abejón, Antonio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {707-722},
publisher = {Unione Matematica Italiana},
title = {Rosenthal and semi-Tauberian linear relations in normed spaces},
url = {http://eudml.org/doc/195428},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Álvarez, Teresa
AU - Martínez-Abejón, Antonio
TI - Rosenthal and semi-Tauberian linear relations in normed spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 707
EP - 722
AB - The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related to Rosenthal linear relations in the same way as Tauberian linear relations are related to weakly compact linear relations. We describe examples and investigate special cases: in particular, $F_{+}$ and strictly singular linear relations.
LA - eng
UR - http://eudml.org/doc/195428
ER -

References

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